That is the vacuum control valve that controls how much vacuum the transmission/transmission modulator gets, when you apply the throttle that valve bleeds out vacuum in a controlled way according to how far the accelerator is depressed. Shifting is propably haywire as a result, do you have enough vac line (couple inches?) on the other side of the green plastic "vacuum dampener" to replace the cracked vac line? By the way that white plastic vac valve is hard to find so go easy.

Any vac leaks are harder on your vac pump also so it's best to find the leaks and fixem.